Chapter 19 Jones, Investments: Analysis and Management Portfolio Selection Chapter 19 Jones, Investments: Analysis and Management 1 1

Portfolio Selection Diversification is key to optimal risk management Analysis required because of the infinite number of portfolios of risky assets How should investors select the best risky portfolio? How could riskless assets be used? 2 2

Building a Portfolio Step 1: Use the Markowitz portfolio selection model to identify optimal combinations Step 2: Consider riskless borrowing and lending possibilities Step 3: Choose the final portfolio based on your preferences for return relative to risk 3 3

Portfolio Theory Optimal diversification takes into account all available information Assumptions in portfolio theory A single investment period (one year) Liquid position (no transaction costs) Preferences based only on a portfolio’s expected return and risk 4 4

An Efficient Portfolio Smallest portfolio risk for a given level of expected return Largest expected return for a given level of portfolio risk From the set of all possible portfolios Only locate and analyze the subset known as the efficient set Lowest risk for given level of return 5 5

An Efficient Portfolio All other portfolios in attainable set are dominated by efficient set Global minimum variance portfolio Smallest risk of the efficient set of portfolios Efficient set Part of the efficient frontier with greater risk than the global minimum variance portfolio 6 6

Efficient Portfolios Efficient frontier or Efficient set (curved line from A to B) Global minimum variance portfolio (represented by point A) B x E(R) A y C Risk =  7 7

Selecting an Optimal Portfolio of Risky Assets Assume investors are risk averse Indifference curves help select from efficient set Description of preferences for risk and return Portfolio combinations which are equally desirable Greater slope implies greater the risk aversion 8 8

Selecting an Optimal Portfolio of Risky Assets Markowitz portfolio selection model Generates a frontier of efficient portfolios which are equally good Does not address the issue of riskless borrowing or lending Different investors will estimate the efficient frontier differently Element of uncertainty in application 9 9

The Single Index Model Relates returns on each security to the returns on a common index, such as the S&P 500 Stock Index Expressed by the following equation Divides return into two components a unique part, i a market-related part, iRM 10 20

The Single Index Model  measures the sensitivity of a stock to stock market movements If securities are only related in their common response to the market Securities covary together only because of their common relationship to the market index Security covariances depend only on market risk and can be written as: 11 21

The Single Index Model Single index model helps split a security’s total risk into Total risk = market risk + unique risk Multi-Index models as an alternative Between the full variance-covariance method of Markowitz and the single-index model 12 22

Selecting Optimal Asset Classes Another way to use Markowitz model is with asset classes Allocation of portfolio assets to broad asset categories Asset class rather than individual security decisions most important for investors Different asset classes offers various returns and levels of risk Correlation coefficients may be quite low 13 10

Borrowing and Lending Possibilities Risk free assets Certain-to-be-earned expected return and a variance of return of zero No correlation with risky assets Usually proxied by a Treasury security Amount to be received at maturity is free of default risk, known with certainty Adding a risk-free asset extends and changes the efficient frontier 14 11

Risk-Free Lending Riskless assets can be combined with any portfolio in the efficient set AB Z implies lending Set of portfolios on line RF to T dominates all portfolios below it L B E(R) T Z X RF A Risk 15 12

Impact of Risk-Free Lending If wRF placed in a risk-free asset Expected portfolio return Risk of the portfolio Expected return and risk of the portfolio with lending is a weighted average 16 13

Borrowing Possibilities Investor no longer restricted to own wealth Interest paid on borrowed money Higher returns sought to cover expense Assume borrowing at RF Risk will increase as the amount of borrowing increases Financial leverage 17 14

The New Efficient Set Risk-free investing and borrowing creates a new set of expected return-risk possibilities Addition of risk-free asset results in A change in the efficient set from an arc to a straight line tangent to the feasible set without the riskless asset Chosen portfolio depends on investor’s risk-return preferences 18 15

Portfolio Choice The more conservative the investor the more is placed in risk-free lending and the less borrowing The more aggressive the investor the less is placed in risk-free lending and the more borrowing Most aggressive investors would use leverage to invest more in portfolio T 19 16

The Separation Theorem Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio Separation Theorem: The investment decision, which risky portfolio to hold, is separate from the financing decision Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio, T 20 17

Separation Theorem All investors Invest in the same portfolio Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF, depending on their preferences Risky portfolios are not tailored to each individual’s taste 21 18

Implications of Portfolio Selection Investors should focus on risk that cannot be managed by diversification Total risk =systematic (nondiversifiable) risk +nonsystematic (diversifiable) risk Systematic risk Variability in a security’s total returns directly associated with economy-wide events Common to virtually all securities 22 19

Nonsystematic Risk Variability of a security’s total return not related to general market variability Diversification decreases this risk The relevant risk of an individual stock is its contribution to the riskiness of a well-diversified portfolio Portfolios rather than individual assets most important 23 20

Portfolio Risk and Diversification Number of securities in portfolio 35 20 Total risk Diversifiable Risk Systematic Risk 10 20 30 40 ...... 100+ Number of securities in portfolio 21